Multiple positive solutions and stability results for nonlinear fractional delay differential equations involving p ‐Laplacian operator

Abstract

In this paper, we study a system of multiple positive solutions and stability results for nonlinear fractional delay differential equations involving ‐Laplacian operator. We derived adequate conditions to ensure that at least three nonnegative solutions exist by applying the conditions of the Leggett–Williams fixed‐point theory and some Green function properties. Due to a small change in time‐delay, we analyzed the Hyers–Ulam stability‐type of the equation. We used Riemann–Liouville fractional differential definition, and we assumed that nonzero delay . In addition, for application purpose, comprehensive examples are given to ensure the effectiveness and feasibility of the results in this paper. Our proposed equation generalize some literature in the system.